Valieva tested positive for the banned substance trimetazidine at the Russian national championships in December 2021 but the result was only made known on February 8, a day after she helped her team win a gold medal at the Beijing Olympics.
WADA, through a tool in the world anti-doping code, has since referred Valieva's case to the Court of Arbitration for Sport after it made no progress with the Russian Anti-Doping Agency (RUSADA) and is not hopeful for a speedy resolution.
"The case now is at CAS, which is not predictable as far as I am concerned for the moment because it will depend on a number of factors related to the case," WADA Director General Olivier Niggli told reporters at a Foundation Board meeting in Montreal.
"Like any case at CAS they can be fast or slow depending on how this is being played by the parties, but as far as we're concerned we'll push for a resolution as quickly as possible but it will take some time for sure."
Last month RUSADA said it would not release the results of the investigation into Valieva's positive test "in order to protect the interests" of the teenage skater.
In her defence, Valieva said the positive test was the result of a mix-up with her grandfather's heart medication.
CAS had cleared Valieva, then 15, to continue competing at the Beijing Games in February, upholding an earlier decision by RUSADA to lift a ban on the skater.
CAS had cited the fact that Valieva was a "protected person" under WADA rules as one of the "exceptional circumstances" underpinning its decision. The CAS ruling did not address the merits of Valieva's drug case.
"We've been following this case closely from the beginning. It was not in our hands, at the first instance the decision was to be taken by the resolution body in Russia," said Niggli.
"We gave them a few deadlines for the case to progress and on the fact that we could not see things moving forward we've used the tool that ... allows WADA to bring cases directly to CAS if we consider that they are not progressing within a reasonable deadline.
"So that's where we are."
The Valieva case cast a shadow on the Russians' participation in Beijing as they already faced increased scrutiny over separate doping sanctions that saw them compete without their flag and national anthem.
